ENERGY TRANSMISSION OVER BREAK WATER - A DESIGN CRITERION?

Wave interaction with multiple bottom-standing rectangular porous structures of different structural parameters is numerically modeled using the multidomain boundary element method and the matched eigenfunction expansion method, while assuming linear water wave theory. The sensitivity of wave reflection and transmission to the wave and structural parameters is analyzed with the objective to maximize wave energy attenuation. Different configurations of multiple structures are tested for maximizing the efficiency of dissipation. Furthermore, wave trapping by multiple porous structures near a sloping rigid wall is studied. Bragg resonance is observed in the case of wave scattering by multiple structures irrespective of wave and structural parameters and is found as proportional to the number of structures deployed. In addition, the study reveals that in the presence of multiple structures, due to more wave energy dissipation, wave transmission in the lee side of the structures is reduced significantly when compared with that observed for a single structure.

Oblique wave scattering by a floating elastic plate over a porous bed in single and two-layer fluid systems

Reflected and transmitted waves in a channel with side porous mattresses

Wave transmission through multilayered porous breakwater under regular and irregular incident waves

The effectiveness of a vertical partial flexible porous membrane wave barrier located near a rigid vertical impermeable seawall for trapping obliquely incident surface gravity waves are analyzed in water of uniform depth under the assumption of linear water wave theory and small amplitude membrane barrier response. From the general formulation of the submerged membrane barrier, results for bottom-standing and surface-piercing barriers are computed and analyzed in special cases. Using the eigenfunction expansion method, the boundary-value problems are converted into series relations and then the required unknowns are obtained using the least squares approximation method. Various physical quantities of interests like reflection coefficient, wave energy dissipation, wave forces acting on the membrane barrier and the seawall are computed and analyzed for different values of the wave and structural parameters. The study will be useful in the design of the membrane wave barrier for the creation of tranquility zone in the lee side of the barrier to protect the seawall.

Scattering of obliquely incident surface gravity waves by an array of partial flexible vertical porous wave barriers of varied configurations is studied in finite water depth and deep water cases. For the mathematical modeling purpose, linearized water wave theory is considered. Firstly, the problem associated with double vertical barriers is handled for a solution. To solve the problem, the associated BVP (boundary value problem) is transformed into a system of Fredholm integral equations of the second kind. By using suitable quadrature formulae, these integral equations are converted to a system of linear algebraic equations. These are solved to compute various important physical quantities associated with wave scattering. The energy identities for both finite water depth and deep water cases are derived. These derived energy identities are used to check the computational accuracy and to quantify the loss of wave energy by the barrier system. Subsequently, the study is extended to deal with wave scattering by multiple non‐identical unequally spaced barriers using wide‐spacing approximation and results for equally spaced identical barriers are obtained as a special case. The methodology is further generalized to deal with Bloch problem to incorporate a periodic array of infinite barriers. Occurrences of Bragg resonance in case of multiple barriers are analyzed. From the results associated with the linearized water wave theory, the second‐order mean wave forces are computed and compared with the first‐order wave forces. The phenomena of cloaking for wave scattering by multiple impervious barriers are discussed for a wide variety of wave and structural parameters. The methodology used in this present study can easily be generalized to solve similar problems that arise in mathematical physics.

In the general problem of plane wave reflection and transmission at a boundary separating two linear viscoelastic media, the mathematical formulas for the reflection and transmission coefficients, the transmission angle, the attenuation vector, etc., are not easily interpretable because they cannot easily be expressed in terms of the basic input parameters (Q, incidence angle, etc.). To gain further insight, we study two special cases in which mathematical simplifications occur. No low-loss approximations are involved. In the first case, the incident wave is homogeneous, and the Q values of the two layers are equal, and we find, among other things, that the reflection and transmission coefficients are the same as the ones for perfect elasticity (they do not involve complex velocities, etc., and are independent of Q). In the second special case, the degree of inhomogeneity of the incident wave approaches its upper limit, and we find that the reflection and transmission coefficients approach constant (complex) values independent of the incidence angle, and that there is almost no ray-bending (refraction) upon transmission of the incident wave through the boundary.

Purpose: This research intends to examine inclined pile structures to analyze the effectiveness of inclined pile structures by analyzing the relationship between the transmission coefficient and wave steepness based on several parameters including pile slope (α), the distance between the piles in one row (D), distance between the top of the piles (b), depth (d), wave height (H) and wave period (T). Theoretical reference: Wave breaking structures are widely used to protect beaches from the impact of sea waves that propagate to coastal areas. Wave breakers are coastal structures that are used to withstand and break the height of waves coming towards the beach, so that the area behind the breakwater does not receive much influence from the waves. When passing through coastal buildings, the waves will be reflected (reflection) and forwarded (transmission). Method: Physical laboratory simulations have been carried out to obtain wave data interacting with the inclined pile structure. Next, energy spectrum analysis was carried out to determine the energy spectrum of incident, reflection and transmission waves from wave probe measurements in the form of time series data. Each energy spectrum is used to see the reflection and transmission capabilities of the pile structure from the reflection and transmission coefficients. Result and Conclusion: From this research it is known that in general Kt has an inverse relationship to wave steepness value (Hi/gT2 and Hi⁄ L). The most effective water level for this breakwater is the average water level. The most effective spacing scenario is α=600 scenario; D=1.69cm; b= 5 cm with a Kt value of 0.652 at Hi/gT2 of 0.006, Kr= 0.103 and Kd= 0.245, so only 65.2% of the waves can pass through the structure, 10.3% is reflected, and 24.5% is removed. Implication of research: These lost waves can be caused by waves traveling through the inclined pile structure, due to collisions between waves or other things. Originality/ value: One of the wave breaker innovations that are being developed is the pile structure. Currently, a lot of research has been carried out regarding upright pile structures.

Transmission and reflection of acoustic waves from a layer of a bubble medium into a liquid is theoretically studied, with subsequent reflection of the waves that arise from the rigid wall. The amplitudes of the emerging waves are determined through the amplitude of the initial wave, analytical expressions are obtained for the coefficients of reflection and transmission of waves across the interfaces.

A two-cell model of search for an evading target

This chapter explores the stress wave transmission and reflection from an incident stress wave , between isotropic solids of different Poisson’s ratio, with special emphasis on systems in which at least one of the solids is auxetic. The dimensionless transmitted stress, in terms of the ratio of transmitted to incident stresses, were investigated for longitudinal stresses in prismatic bars (1D stress), longitudinal stresses in width-constrained plates (2D stress or 2D strain), plane waves of dilatation (1D strain), torsional waves (shear waves), and Rayleigh (surface) waves. Each of these wave transmission study was performed under three special cases, i.e. when the (i) product of density and Young’s modulus for both solids are equal, (ii) product of density and shear modulus for both solids are equal, and (iii) product of density and bulk modulus for both solids are equal. Under these special conditions, results show that the stress transmission is effectively doubled or eliminated when the Poisson’s ratio for the isotropic solids are at their limits.

Hydrodynamic performance of a novel WEC-breakwater integrated system consisting of triple dual-freedom pontoons

An analytical solution is developed to investigate the behavior of a submerged or surface-piercing, long tethered breakwater of rectangular cross section. The equations of motion are solved to provide the surge, heave, and pitch responses of the structure. The wave reflection and transmission coefficients are calculated. Numerical results are presented for a range of wave and geometric parameters that illustrate the suitability of this type of structure as a barrier to wave action. Small-scale physical model tests were carried out to verify the theory. Reasonable agreement is found between theoretical and experimental values of the reflection and transmission coefficients. It was observed both in the numerical results and model tests that low wave transmission coefficients occur when the diffracted and radiated waves in the lee of the structure are of similar magnitude, but 180° out of phase. The lowest transmission coefficients occurred near the surge natural frequency of the floating breakwater, where significant energy dissipation was present. Under these circumstances, destructive wave interference and energy dissipation combine to give transmission coefficients on the order of 0.5.

To evaluate the effect of weight reduction on the structural and functional parameters of the optic nerve in established cases of papilledema in Idiopathic Intracranial Hypertension (IIH). A prospective observational study in early and established cases of papilledema in IIH presenting from December 2019 to February 2021. Functional parameters (visual acuity, contrast sensitivity, mean deviation, VER), structural parameters (RNFL, GCL-IPL, and optic disc height), and clinical grading of papilledema were measured at baseline and every 6 weeks for 6 months. All patients underwent medical (oral acetazolamide) and diet therapy. Mean body mass index (BMI) at presentation was 26.32 ± 3.52 kg/m² and the mean change in BMI over 6 months was 1.27 ± 0.50 kg/m². 67% of eyes had papilledema of grades 2-3 at the presentation. At the end of 6 months, 75% of eyes had grade 1 papilledema while 13% showed complete resolution. A reduction of 5.32 ± 3.58 in mean deviation (r = 0.316; p-value 0.01) and gain in VER P100 amplitude of 4.2 ± 2.7 µV (r = 0.40; p-value 0.003) were noted over 6 months with reduction in BMI over 6 months. A statistically significant reduction in optic disc height (ODH) was noticed with BMI reduction over 6 months (p = 0.0007; r = 0.45).A reduction of 1.72 ± 0.90 kg/m² (equivalent to 6.53% weight loss) in BMI was associated with a four-grade change in clinical grading of papilledema. Reduction in BMI had a significant impact on both structural and functional parameters of the optic nerve in IIH. The involvement of a well-certified dietician should be an integral part of treatment in IIH.

SUMMARY The reflection and transmission of elastic waves are of great significance for predicting reservoir physical properties, interpreting seismic data and detecting crustal structures. Most studies only consider the initial vertical stress state when studying the reflection and transmission of elastic waves at imperfectly bonded interfaces, but few studies consider the influence of initial stress on boundary conditions. Moreover, the effect of initial stress on the energy distribution of elastic waves at imperfectly bonded interfaces has rarely been investigated. We propose a unified method to calculate the energy reflection and transmission coefficients for different incident waves at welded or imperfectly bonded interfaces in stressed media. The effects of initial stress on the equation of motion, the elastic properties of the medium and the boundary conditions at the interface are considered. The elastic properties of rocks under initial stress are described by acoustoelasticity theory. In addition, we define a new stress tensor to modify the linear-slip model for describing boundary conditions at the imperfectly bonded interface in the presence of initial stress. Numerical results show that the energy reflection and transmission coefficients at the non-welded interface in stressed media depend on the elastic properties of the incident and transmitted media, the initial stress, the type and magnitude of the interfacial compliance and the frequency and propagation direction of the incident wave. The initial vertical and horizontal stresses dominate the reflection and transmission coefficients at small and large angles, respectively. The discontinuity in displacement across the imperfectly bonded boundary results in the frequency dependence of the reflection and transmission coefficients. Imperfect bonding enhances P-wave and SV-wave energy reflection and weakens P-wave energy transmission. However, imperfect bonding can enhance the energy transmission of the SV wave for the imperfectly bonded interface with high contrast between tangential and normal compliance and a resonance peak appears at a specific frequency. We also notice that imperfectly bonded interfaces with interfacial compliance less than $1.0 \times {10}^{ - 11}$ m Pa−1 can be regarded as welded interfaces in the seismic frequency band (lower than 100 Hz). In addition, the initial stress greatly influences the reflection coefficients at high frequencies and the transmission coefficients at low frequencies. The initial vertical stress can reduce the energy transmission of SV waves at imperfectly bonded interfaces. In contrast, the initial horizontal stress can significantly increase the energy transmission of low-frequency SV waves and may lead to the disappearance of the resonant peak in the transmission coefficients.